{"paper":{"title":"Multiphase-Linear Ranking Functions and their Relation to Recurrent Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.PL","authors_text":"Amir M. Ben-Amram, Jes\\'us J. Dom\\'enech, Samir Genaim","submitted_at":"2018-11-18T15:34:16Z","abstract_excerpt":"Multiphase ranking functions (M$\\Phi$RFs) are tuples $\\langle f_1,\\ldots,f_d \\rangle$ of linear functions that are often used to prove termination of loops in which the computation progresses through a number of \"phases\". Our work provides new insights regarding such functions for loops described by a conjunction of linear constraints (Single-Path Constraint loops). The decision problem existence of a M$\\Phi$RF asks to determine whether a given SLC loop admits a M$\\Phi$RF, and the corresponding bounded decision problem restricts the search to M$\\Phi$RFs of depth $d$, where the parameter $d$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07340","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}